On the Prime Spectrum of an Integral Domain with Finite Spectral Semistar Operations

Abstract

In this paper, we investigate the prime spectrum of an integral domain R with a finite number of spectral semistar operations. This will be done by seeking for a possible link between the cardinality of the set SpSS (R) of all spectral semistar operations on R and its Krull dimension. In particular, we prove that if | SpSS (R)|=n+ dim R, then 2| Max (R)|≤ n+1. This leads us to give a complete description for the spectrum of a domain R such that | SpSS (R)|=n+ dim R for 1 ≤ n ≤ 5.